Theorems · Inductive type · algebraic topology
SSet.Subcomplex.Pairing.RankFunction.Cell
{X : SSet} →
{A : X.Subcomplex} → {P : A.Pairing} → {ι : Type v} → [inst : LinearOrder ι] → P.RankFunction ι → ι → Type uGiven a rank function f : P.RankFunction ι for a
pairing P of a subcomplex A of X : SSet, and i : ι,
this is the type of type (II) simplices of rank i.
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement · cited by 8,572
- SSetstatement · cited by 1,283
- SSet.Subcomplexstatement · cited by 461
- SSet.Subcomplex.Pairingstatement · cited by 117
- SSet.Subcomplex.Pairing.RankFunctionstatement · cited by 68
Cited by79
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.Pairing.RankFunction.Cell.dimstatement and proof · cited by 40
- SSet.Subcomplex.Pairing.RankFunction.filtrationproof · cited by 34
- SSet.Subcomplex.Pairing.RankFunction.Cell.sstatement and proof · cited by 21
- SSet.Subcomplex.Pairing.RankFunction.sigmaStdSimplexproof · cited by 21
- SSet.Subcomplex.Pairing.RankFunction.Cell.hornstatement and proof · cited by 19
- SSet.Subcomplex.Pairing.RankFunction.sigmaHornproof · cited by 18
- SSet.Subcomplex.Pairing.RankFunction.Cell.ιSigmaStdSimplexstatement and proof · cited by 16
- SSet.Subcomplex.Pairing.RankFunction.bproof · cited by 13
- SSet.Subcomplex.Pairing.RankFunction.Cell.mapstatement and proof · cited by 12
- SSet.Subcomplex.Pairing.RankFunction.Cell.indexstatement and proof · cited by 10
- SSet.Subcomplex.Pairing.RankFunction.Cell.ιSigmaHornstatement and proof · cited by 10
- SSet.Subcomplex.Pairing.RankFunction.Cell.mapToSuccstatement and proof · cited by 9